This paper presents a stabilization technique for the finite element modeling of contact-impact problems of elastic bars via a bi-penalty method for enforcing contact constraints while employing an explicit predictor–corrector time integration algorithms. The present proposed method combines three salient features in carrying out explicit transient analysis of contact-impact problems: the addition of a penalty term associated with a kinetic energy expression of gap constraints, in addition to the conventional internal energy penalty term of the gap constraints; an explicit integration method that alleviates spurious oscillations; and, a judicious selection of two penalty parameters such that the stable time steps of the resulting explicit method is least compromised. Numerical experiments have been carried out with three explicit methods: the standard central difference method, the stabilized predictor-predictor method (Wu, 2003 [1]) and a method for mitigating spurious oscillations (Park et al., 2012) as applied to simulate one-dimensional contact-impact problems of the Signorini problem and the impact of two elastic bars. Results indicates that the proposed method can maintain the contact-free stability limit of the central difference and yield improved accuracy compared with existing bi-penalty methods.

本文提出了一种基于双罚法的弹性杆接触碰撞问题有限元建模的稳定技术。在采用显式的预测器-校正器时间积分算法时，可以加强接触约束。在对接触碰撞问题进行显式瞬态分析时，本文提出的方法结合了三个显着特征：除了间隙约束的常规内部能量惩罚项外，还增加了与间隙约束的动能表达相关的惩罚项；一种显式积分方法，可减轻寄生振荡；明智地选择两个惩罚参数，以使最终显式方法的稳定时间步长受到最小程度的损害。使用三种显式方法进行了数值实验：标准中心差方法，稳定的预测器-预测器方法（Wu，2003 [1]）和一种减轻杂散振荡的方法（Park等，2012），用于模拟Signorini问题的一维接触碰撞问题以及两个弹性杆的冲击。结果表明，与现有的双罚方法相比，该方法可以保持中心差的无接触稳定性极限，并提高了精度。